swanson mean is error prone for distribution other than normal

  • Swanson’s mean (SM) has no theoretical justification for any distribution other than the normal.

    • This is despite it is being heavily used within the oil and gas industry to approximate continuous probability such as the log-normal.
    • SPE paper SPE-148542-PA (see references below) document the errors induced by this practice. The studies discussed in the preceding demonstrated the rule’s inability to accurately approximate the variance of many distributions
    • Bear in mind that MCS was never recommended as a final approximation, as ESM has been

  • The equal-areas method was developed to apply to normal distribution that produces an approximation of 25%-50%-25% for P89.9-P50-P10.2

    • It was developed by Jim Matheson and his colleagues at the Stanford Research Institute (SRI) between the late 1960s and the early 1970s (personal communication with Jim Matheson and Peter McNamee).
    • On the basis of this, SRI began using a shortcut of weighting the P90, P50, P10 by 0.25, 0.50, 0.25, which is sometimes referred to at the 25-50-25 approximation. This method was then heavily used and popularized by Strategic Decisions Group (SDG), which was founded by individuals from SRI's decision analysis group.
    • SDG trained hundreds of oil and gas professionals in decision analysis methods and helped to establish existing decision analysis programs at several major corporations, including Chevron; this explains the use of 25-50-25 in oil and gas settings.

  • SM can be directly applied to log-normal distributions by applying it to the logarithm of X, instead of directly to X.

    • If X is log-normally distributed, then ln X is normally distributed and the moments of X are functions only of the mean μ and variance σ_2 of ln _X.
    • This log-SM approximation is a significant improvement over SM and is only slightly more complicated—requiring the use of a logarithm and of an exponential.

Other paper supporting the inaccuracy of Swanson’s Rule

  • Megill (1984)

    • finds that ESM underestimates the mean by approximately 10% for modestly skewed distributions and 45% for more-skewed distribution
    • Modestly skewed distributions, which he associates with “typical prospect ranges.”, while more-skewed distributions, which he associates with “typical basin-play ranges for field size distributions.”
    • Megill concludes that “Swanson’s rule should not be applied to obtain the mean of play or basin assessments.”

  • Rose (2001)

    • supports his use of ESM by arguing that reserves above the P1 of a log-normal occur with much less than a 1% frequency, and therefore the log-normal should be truncated above this point. Doing so reduces skewness and does improve the accuracy of ESM.
    • However, Rose supports his argument by analyzing only the mean and examining a single log-normal distribution with a mean of 15.1 and a standard deviation of 28.2—implying a skewness of 3.9. In this case, ESM underestimates the true mean by 1.5%.
    • However, it also underestimates the variance by 59% and the skewness by 78%. Furthermore, under a different truncated log-normal distribution with a skewness of 4.9, ESM underestimates the mean by 10%, the variance by 77%, and the skewness by 83%. SM can be directly applied to log-normal distributions by applying it to the logarithm of X, instead of directly to X. If X is log-normally distributed, then ln X is normally distributed and the moments of X are functions only of the mean µ and variance 2 of ln X. The equations for the first four moments of X appear below:

References

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  • topic:: 00 Engineering Economics00 Engineering Economics
    #MOC / for economics notes with focus on petroleum fiscal and engineering
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